Question

The least positive number k for which x=k is an asymptote for the tangent function is ___?

Answer 1

The least positive number k for which x=k is an asymptote for the tangent function is π/2 (or 90 degrees), which is the first instance where the cosine function equals zero.

Step-by-step explanation:

The student is asking about the asymptotes of the tangent function. In trigonometry, the tangent function has vertical asymptotes at points where the cosine function equals zero since the tangent function is the ratio of the sine to the cosine functions. The least positive number k for which x=k is an asymptote for the tangent function is at π/2 radians (or 90 degrees), as this is the smallest positive value for which the cosine function is zero, thereby causing the tangent function to be undefined and approach infinity. For all vertical asymptotes of the tangent function, they occur at odd integer multiples of π/2. Therefore, the requested value of k would be π/2.

Answer 2

The least positive number k for which x=k is an asymptote for the tangent function is π/2 (pi/2) or approximately 1.5708.

Step-by-step explanation:

The least positive number k for which x=k is an asymptote for the tangent function is π/2 (pi divided by 2) or approximately 1.5708. The tangent function, tan(x), has asymptotes at x = (2n+1)π/2 for every integer n. These are the values for which the cosine function is zero, making the tangent undefined. Because we are looking for the least positive number, we use n=0 which gives us x = π/2 as the first positive asymptote to the right of the origin.